Exam 8: The Unit Circle and Functions of Trigonometry

If $\tan \theta=\frac{4}{3}$ and $\theta$ is in quadrant III find the values of the other trigonometric functions of $\theta$ .

graph the given function over a two-period interval. Identify asymptotes when applicable. -The average monthly high temperature (in $\mathrm{F}^{\circ}$ ) in Paris can be modeled using the trigonometric function defined by $f(x)=16.5 \sin \left[\frac{\pi}{6}(x-4.1)\right]+59.5$ , where $x$ is the month and $x=1$ corresponds to January. (a) Graph $f$ over the interval $1 \leq x \leq 25$ . (b) Determine the amplitude, period, phase shift, and vertical translation of $f$ . (c) What is the average monthly high temperature for the month of October? (d) Find the maximum and minimum average monthly high temperatures and the months when they occur. (e) What would be an approximation for the average yearly high temperature in Paris? How is this related to the vertical translation of the sine function in the formula for $f$ ?

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=2 \sin \left(x-\frac{\pi}{2}\right)+1$

Find the angle of smallest positive measure coterminal with $-828^{\circ}$ .

Find the length of an arc intercepted by an angle of $85^{\circ}$ in a circle with radius 19 inches. graph the given function over a two-period interval. Identify asymptotes when applicable.

Use a calculator to approximate $\theta$ to the nearest tenth in the interval $\left[0,90^{\circ}\right]$ , if $\cos \theta=0.9086146585$ .

Find the angle of smallest positive measure coterminal with $-634^{\circ}$ .

(a) Convert $315^{\circ}$ to radians. (b) Convert $\frac{11 \pi}{12}$ to degrees.

If $(-5,-6)$ is on the terminal side of angle $\theta$ in standard position, find $\sin \theta, \cos \theta$ , and $\tan \theta$ .

Find the angle of smallest positive measure coterminal with $-559^{\circ}$ .

Use the figure to find the following: (a) The smallest positive angle coterminal with $\theta$ . (b) The values of $x$ and $y$ . (c) The values of the six trigonometric functions of $\theta$ . (d) The radian measure of $\theta$ .

graph the given function over a two-period interval. Identify asymptotes when applicable -The average monthly low temperature (in $\mathrm{F}^{\circ}$ ) in Paris can be modeled using the trigonometric function defined by $f(x)=12 \sin \left[\frac{\pi}{6}(x-4.1)\right]+46$ , where $x$ is the month and $x=1$ corresponds to January. (a) Graph $f$ over the interval $1 \leq x \leq 25$ . (b) Determine the amplitude, period, phase shift, and vertical translation of $f$ . (c) What is the average monthly low temperature for the month of October? (d) Find the maximum and minimum average monthly low temperatures and the months when they occur. (e) What would be an approximation for the average yearly low temperature in Paris? How is this related to the vertical translation of the sine function in the formula for $f$ ?

Solve the triangle.

A central angle of a circle with radius 45 centimeters cuts off an arc of 165 centimeters. Find each measure. (a) The radian measure of the angle. (b) The area of the sector with this central angle.

If $\cos \theta<0$ and $\tan \theta>0$ , in which quadrant does $\theta$ lie?

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=-\cos 4 x$

Use the figure to find the following: (a) The smallest positive angle coterminal with $\theta$ . (b) The values of $x$ and $y$ . (c) The values of the six trigonometric functions of $\theta$ . (d) The radian measure of $\theta$ .

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=2 \sin \left(x+\frac{\pi}{2}\right)+1$

Use the figure to find the following: (a) The smallest positive angle coterminal with $\theta$ .. (b) The values of $x$ and $y$ . (c) The values of the six trigonometric functions of $\theta$ (d) The radian measure of $\theta$ .

Find the length of an arc intercepted by an angle of $235^{\circ}$ in a circle with radius 27 inches.